(04.02 LC)
The graph below shows the numbers of cups of grape juice that are mixed with cups of lemon-lime soda to make servings of grape soda:
A graph is shown. The values on the x-axis are 0, 1, 2, 3, 4, 5. The values on the y-axis are 0, 2, 4, 6, 8, 10. Points are shown on ordered pairs 0, 0 and 1, 2 and 2, 4 and 3, 6 and 4, 8. These points are connected by a line. The label on the x-axis is Lemon lime Soda in cups. The title on the y-axis is Grape Juice in cups.
What is the ratio of the number of cups of grape juice to the number of cups of lemon-lime soda?
using the points, the x is Soda and the Y is the grape juice
for (1,2) 1 soda to 2 juices
(2,4) 2 sodas to 4 juices
so the ratio is 2 juices to every 1 soda which is a 2/1 ratio
Answer:
C
Step-by-step explanation:
(x x y)a = xa x ya illustrates which property of eponents
Find slope of horizontal and vertical lines
If I am choosing an outfit to wear, are the events "collared shirt" and "Long-sleeved shirt" Mutually exclusive or Inclusive? Mutually Exclusive Inclusive
The student store sells pencils that have a markup of 120 percent above their wholesale cost of $0.50 each. They also charge sales tax of 8 percent. What is the total cost of a pencil from the student store?
Answer:
The total cost of a pencil from the student store is $ 1.188
Step-by-step explanation:
Given,
The original cost or wholesale cost of each pencil = $ 0.50,
Markup percentage = 120 %,
So, the cost of the pencil after markup = 0.50 + 120% of 0.50
[tex]=0.50+\frac{120\times 0.50}{100}[/tex]
[tex]=0.50+\frac{60}{100}[/tex]
[tex]=0.50+0.6[/tex]
[tex]=1.1[/tex]
Now, sales tax = 8 %,
Hence, the final total cost of a pencil = 1.1 + 8 % of 1.1
[tex]=1.1 + \frac{8\times 1.1}{100}[/tex]
[tex]=1.1+\frac{8.8}{100}[/tex]
[tex]=1.1+0.088[/tex]
[tex]=\$1.188[/tex]
Explain why you would make one of the addends a tens number when solving an addition problem.
Since we can add a number to a tens number easily, we make one of the addends a tens number when solving an addition problem.
Example 1:
Add 9 and 6.
9 + 6 = 9 + (1 + 5)
= (9 + 1) + 5
= 10 + 5 = 15
Note that adding 10 and 5 is much easier than adding 9 and 6.
Example 2:
Add 18 and 16.
18 + 16 = 18 + (2 + 14)
= (18 + 2) + 14
= 20 + 14 = 34
Note that adding 20 and 14 is much easier than adding 18 and 16.
in chemistry, n molecules of an ideal gas have pressure (p), volume (v), and temperature (T) that stand in the following relation, where R is a constant. solve the equation for n, the number of molecules. PV= nRT
A landscaper buys a tree that grows at a rate of 18 inches every 3 months.
How much does it grow in 1 year?
A. 30 in.
B. 36 in.
C. 54 in.
D. 72 in.
A plant grows 9 in. every 2 months.
How will it grow in a year?
A. 18 in.
B. 36 in.
C. 54 in.
D. 108 in.
1 it grows 18 inches every 3 months
there are 12 months in 1 year
12 dived by 3 = 4 so there are 4 times it will grow 18 inches
18 * 4 = 72 inches, amount it grows in 1 year
Answer is D
2. it grows 9 inches every 2 months
12/2 = 6 times a year it will grow
9 *6 = 54 inches total for 1 year
Answer is C
Marko can bike at an average speed of 5 3\4 min/mi. He bikes at this speed for 86 1\4 min. How many miles does Marko bike
Answer: 15
Step-by-step explanation: k12 Interim Checkpoint: Grade 6 Checkpoint 1 - Part 1
Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each. He also bought a roll of fancy wrapping paper containing 4.18 square meters. How much paper did he have altogether?
Answer:
The answer is 24.28 square meters.
Step-by-step explanation:
Kwan bought three rolls of regular wrapping paper with 6.7 square meters of paper each.
The paper in three rolls become = [tex]3\times6.7=20.1[/tex] square meter
He also bought a roll of fancy wrapping paper containing 4.18 square meters.
So, total paper that Kwan had is = [tex]20.1+4.18=24.28[/tex] square meter.
Therefore, the answer is 24.28 square meters.
Answer: The answer is 20.1
Step-by-step explanation: To find out how much paper Kwan had altogether, we need to calculate each type's total square meters of wrapping paper and then add them together.
Kwan bought three rolls of regular wrapping paper, each with 6.7 square meters of paper. To find the total square meters for the traditional wrapping paper, we can multiply the number of rolls (3) by the square meters per roll (6.7):
3 rolls * 6.7 square meters/roll = 20.1 square meters
So, Kwan has 20.1 square meters of regular wrapping paper.
In addition, Kwan also bought a roll of fancy wrapping paper, which contains 4.18 square meters.
To find the total amount of wrapping paper Kwan has, we can add the square meters of regular wrapping paper to the square meters of fancy wrapping paper:
Evaluate 8a^3b^-2 for a=4 and b=-5
To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, substitute the given values into the expression and simplify to obtain the final result, which is 16.32.
Explanation:To evaluate 8[tex]a^3b^{-2[/tex] for a=4 and b=-5, we substitute the given values into the expression. Plugging in these values, we have:
8[tex](4)^3(-5)^{(-2)[/tex]
Simplifying this expression, we get:
8(64)(1/[tex](-5)^2)[/tex]
The next step is to calculate the value of [tex](-5)^2[/tex], which equals 25. So the expression becomes:
8(64)(1/25)
Then, multiplying 64 by 1/25, we get:
8(64/25)
Finally, multiplying 8 by 64/25, we obtain:
16.32
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The figure below shows a transversal t which intersects the parallel lines PQ and RS:
Write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8.
Answer:
For the proof, check the explanation part.
Step-by-step explanation:
In the given figure, the lines PQ and RS are parallel and line t is transversal.
It is required to prove that measure of angle 4 is equal to measure of angle 8.
Now, measure of angle 4 will be equal to measure of angle 6 because they are the alternate interior angles.
Now, the measure of angle 6 will be equal to measure of angle 8 because they are the vertically opposite angles.
So, form the above information, it can be concluded that,
[tex]\angle 4=\angle 6\\\angle 6=\angle 8\\\angle 4=\angle 8[/tex]
Hence proved.
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Can someone help me with this problem?
Which expression is the completely factored form of x6−64y3 ? (x2−4y)(x4−16y2) (x2−4y)3 (x2−4y)(x4+4x2y+16y2) (x2+4y)(x4−4x2y+16y2)
The expression which is obtained on factorising it completely is:
[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]
Step-by-step explanation:We are asked to factorize the expression which is given by:
[tex]x^6-64y^3[/tex]
This expression could also be written as:
[tex]x^6-64y^3=(x^2)^3-(4y)^3[/tex]
Now, we know that:
[tex]a^3-b^3=(a-b)(a^2+b^2+ab)[/tex]
Here we have:
[tex]a=x^2\\\\and\\\\b=4y[/tex]
Hence,
[tex]x^6-64y^3=(x^2-4y)((x^2)^2+(4y)^2+x^2\times 4y)[/tex]
i.e.
[tex]x^6-64y^3=(x^2-4y)(x^4+16y^2+4x^2y)[/tex]
A number divided by 80 has a quotient of 7 with 4 as a remainder. Find the number.
Answer:
564
Step-by-step explanation:
80 x 7 = 560 + 4 = 564
Divsor Answer Remainder Divident
Therefore, the number is 564.
The quotient of 12 and opposite of 3 plus the product of the opposite of 14 and 4
What's the area of the triangle below
Answer:
Option (a) is correct.
The area of triangle is 24 m²
Step-by-step explanation:
Given : A triangle with base 6 m and height 8 m
We have to find the area of the triangle and choose the correct option from the given options.
Area of triangle = [tex]\frac{1}{2}\cdot base\cdot height[/tex]
Given Base = 6 m
and height = 8 m
Therefore, Area of triangle = [tex]\frac{1}{2}\cdot 6\cdot 8=24[/tex]
Thus, The area of triangle is 24 m²
The correct option is [tex]\boxed{\bf option A}[/tex] i.e., the area of triangle is [tex]\boxed{\bf 24\text{\ \bf m}^{2}}[/tex].
Further explanation:
We are given the base and height of the triangle as shown in the given figure.
If the height and base of a triangle is given then the area of the triangle can be calculated by the formula given below,
[tex]\boxed{\text{Area of Triangle}=\dfrac{1}{2}\cdot \text{base}\cdot \text{height}}[/tex] .....(1)
Calculation:
Here, the height of the triangle is [tex]8\text{ m}[/tex] and base of the triangle is [tex]6\text{ m}[/tex].
Substitute the value of height that as [tex]8\text{ m}[/tex] and the value of base that as [tex]6\text{ m}[/tex] in equation (1) to obtain the area of the triangle as follows:
[tex]\begin{aligned}\text{Area of Triangle}&=\dfrac{1}{2}\cdot 6\cdot 8\\&=\dfrac{48}{2}\\&=24\end{aligned}[/tex]
Therefore, the area of the triangle is [tex]\boxed{\bf 24\text{\ \bf m}^{2}}[/tex].
This implies that the correct option is [tex]\boxed{\bf option A}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Triangle
Keywords: Triangles, area, height, base, volume, heron’s formula, edges, vertices, collinear, non-collinear, geometry, equilateral triangles, isosceles triangle, right angled triangle, angles, Pythagoras theorem, acute angle, obtuse triangle, congruent triangles, similar triangles.
What is the value of 4 in 783,549,201
50 POINTS FOR WHOEVER ANSWERS CORRECTLY!!!!! Rotate these coordinates 270 degrees counterclockwise around the origin and then translate 5 units up.
What is the algebraic expression that describes the monthly salary? Let x be the hours of training
Movie rental at a video store, you have two options for renting movies. You can pay $4 per movie,or you can pay a one time membership fee of $20 and then pay only $1.50 per movie. After how many movie rentals will she cost of renting movies with the membership be less than the cost of renting movies without the membership?
After 8 movie rentals, will the cost of renting movies with the membership be less than the cost of renting movies without the membership.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
There are two options for renting movies.
As per the first option,
Pay $4 per movie, so the equation will be,
y = 4x (i)
Where y is the total cost and x is the number of movies.
As per the second option,
Take a membership of $20, and they pay $1.50 per movie.
So, the equation will be,
y = 1.5x + $20 (ii)
Where y is the total cost and x is the number of movies.
Now, solve equations (i) and (ii)
4x = 1.5x + $20
4x - 1.5x = 20
2.5x = 20
x = 20/2.5
x = 8
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What is 1,120 divided by 35
Two cars leave the same location traveling in opposite directions. One car leaves at 3:00 p.m. traveling at an average rate of 55 miles per hour. The other car leaves at 4:00 p.m. traveling at an average rate of 75 miles per hour. Let x represent the number of hours after the first car leaves.
How many hours after the first car leaves will the two cars be 380 miles apart?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the number of hours in the second box.
Solution-
Two cars leave the same location traveling in opposite directions.
The first car leaves at 3 p.m and has a speed of 55 mph
The second car leaves at 4 p.m and has a speed of 75 mph
Let x hours after the first car leaves, the two cars are 380 miles apart from each other.
[tex]Speed =\frac{Distance}{Time}[/tex]
[tex]\Rightarrow Distance=Speed\times Time[/tex]
In this x hours, distance covered by the first car,
[tex]\Rightarrow Distance_1=Speed_1\times Time_1[/tex]
[tex]\Rightarrow Distance_1=55\times x[/tex]
As the second car leaves at 4 p.m i.e 1 hour late as compared to the first car, so distance covered by the second car in (x-1) hours,
[tex]\Rightarrow Distance_2=Speed_2\times Time_2[/tex]
[tex]\Rightarrow Distance_2=75\times (x-1)[/tex]
According to the question,
[tex]Distance_1+Distance_2=380[/tex]
[tex]\Rightarrow 55\times x+75\times (x-1)=380[/tex]
[tex]\Rightarrow 55x+75x-75=380[/tex]
[tex]\Rightarrow 130x=455[/tex]
[tex]\Rightarrow x=3.5[/tex]
∴ After 3.5 hours from 3 p.m i.e at 6.5 p.m the cars will have a distance of 380 miles.
Anne Katz, the owner of Katz Sport Shop, lends $8,000 to Shelley Slater to help her open an art shop. Shelley plans to repay Anne at the end of eight years with interest compounded semiannually at 8%. At the end of eight years, Anne will receive (use the tables in the handbook):
$14,984
$16,857
$16,587
$14,484
None of these
In a load of laundry, 60% of the socks are white. If there are 25 socks in the load, how many are white?
Answer:
15
Step-by-step explanation:
You have to multiply 0.60 by 25 in order to get 15! Easy, right?
Twenty-five students go to lunch. Pizza costs $3 and sandwiches cost $2. Twelve students buy pizza. What is the total amount of money spent on sandwiches?
The total amount of money spent on sandwiches is $26.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, Twenty-five students go to lunch. The pizza costs $3 and the sandwiches cost $2.
Twelve students buy pizza.
∴ 13 students bought sandwiches.
So, The total money they spent on Pizza and Sandwiches is (3×12) + (2×13) = 36 + 26 = $52.
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Which type of line symmetry does the letter "W" have?
horizontal
diagonal
vertical
none of the above
The perimeter of a rectangle is 38 inches. If the length of the rectangle is 11 inches, which equation could be used to find the width, x?
A.
11(x + 2) = 38
B.
2(x + 11) = 38
C.
x + 2(11) = 38
D.
x + 11 = 38
The product of two ratio rational numbers is 48/5. If one of the rational number is 66/7, find the other rational number.
Final answer:
The other rational number is 384/7.
Explanation:
To find the other rational number, we can set up a proportion by setting the two ratios equal to each other. The given ratio is 66/7, and the product of the two ratios is 48/5.
Let the other rational number be represented by w. Writing the proportion, we have:
66/7 = w/(48/5)
Cross multiplying and solving for w:
w = (66/7) * (48/5)
w = 8*48/7
w = 384/7
Hence, the other rational number is 384/7.
What is 1/6×2/3= to what